Remember that every fraction represents a division: the numerator divided by the denominator.
For example,
We can use this idea to rewrite expressions containing fractions.
For example, suppose we want to rewrite the following expression:
Interpreting the fraction as division, we can write our expression as
Next, we use the fact that we can swap the order of multiplication and division. So, we can write an equivalent expression by switching the and the as follows:
Therefore,
What is missing from the statement below?
Interpreting the fraction as division, we can write our expression as:
We can write an equivalent expression by swapping the and the Therefore, the missing part is
What is missing from the statement below?
\[ \dfrac{4}{3}\times 9 = 4 \times \bbox[2pt, border:1pt solid black]{\phantom{A}} \div \bbox[2pt, border:1pt solid black]{\phantom{A}} \]
|
a
|
$1 \div 3$ |
|
b
|
$9 \div 3$ |
|
c
|
$3 \div 9$ |
|
d
|
$3 \div 4$ |
|
e
|
$4 \div 9$ |
What is missing from the statement below? \[ 6 \times \dfrac{2}{3} = \bbox[2pt, border:1pt solid black]{\phantom{A}} \div \bbox[2pt, border:1pt solid black]{\phantom{A}} \times 2 \]
|
a
|
$6 \div 3$ |
|
b
|
$3 \div 6$ |
|
c
|
$3 \div 2$ |
|
d
|
$2 \div 6$ |
|
e
|
$2 \div 3$ |
Consider the expression By expressing the fraction as division, we have
and by swapping the and the we have
Now, notice that we can rewrite the division as a new fraction to produce a new expression:
Therefore,
What fraction is missing from the statement below?
We can write an equivalent expression by swapping the and the
We can now interpret the division as a fraction:
So, the missing fraction is
What fraction is missing from the statement below?
\[ 2\div 3\times 9 =2\times \dfrac{\fbox{$\,\phantom{0}\,$}}{\fbox{$\,\phantom{0}\,$}} \]
|
a
|
$\dfrac{9}{2}$ |
|
b
|
$\dfrac{9}{3}$ |
|
c
|
$\dfrac{1}{3}$ |
|
d
|
$\dfrac{3}{9}$ |
|
e
|
$\dfrac{2}{9}$ |
What fraction is missing from the statement below?
\[ 3\div 2\times 4 = 3\times \dfrac{\fbox{$\,\phantom{0}\,$}}{\fbox{$\,\phantom{0}\,$}} \]
|
a
|
$\dfrac{1}{2}$ |
|
b
|
$\dfrac{1}{8}$ |
|
c
|
$\dfrac{4}{2}$ |
|
d
|
$\dfrac{2}{4}$ |
|
e
|
$\dfrac{8}{1}$ |
What fraction is missing from the statement below?
Interpreting the fraction as division, we can write our expression as:
We can write an equivalent expression by swapping the and the
Finally, we can write the as a fraction:
What fraction is missing from the statement below? \[ \dfrac{5}{3}\times 6= 5 \times \dfrac{\bbox[2pt, border:1pt solid black]{\phantom{A}}}{\bbox[2pt, border:1pt solid black]{\phantom{A}}} \]
|
a
|
$\dfrac{3}{5}$ |
|
b
|
$\dfrac{3}{6}$ |
|
c
|
$\dfrac{6}{3}$ |
|
d
|
$\dfrac{5}{3}$ |
|
e
|
$\dfrac{1}{3}$ |
What fraction is missing from the statement below? \[ 18 \times \dfrac{1}{9} = \dfrac{\bbox[2pt, border:1pt solid black]{\phantom{A}}}{\bbox[2pt, border:1pt solid black]{\phantom{A}}} \times 1 \]
|
a
|
$\dfrac{9}{1}$ |
|
b
|
$\dfrac{1}{9}$ |
|
c
|
$\dfrac{9}{18}$ |
|
d
|
$\dfrac{18}{1}$ |
|
e
|
$\dfrac{18}{9}$ |
Let's evaluate the following expression:
First, by swapping the order of multiplication and division, we can rewrite our expression as
Now, notice that is a factor of and
Therefore, we can evaluate our entire expression as follows:
Evaluate
Interpreting the fraction as division, we can write our expression as:
We can write an equivalent expression by swapping the and the
Expressing the division as a fraction, we arrive at:
We now solve:
$12 \times \dfrac{7}{4}=$
|
a
|
$32$ |
|
b
|
$18$ |
|
c
|
$24$ |
|
d
|
$16$ |
|
e
|
$21$ |
$\dfrac{3}{4}\times 36=$
|
a
|
$28$ |
|
b
|
$30$ |
|
c
|
$27$ |
|
d
|
$18$ |
|
e
|
$24$ |